Related papers: Geometry-Informed Neural Operator for Large-Scale …

Current neural operators often struggle to generalize to complex, out-of-distribution conditions, limiting their ability in seismic wavefield representation. To address this, we propose a generative neural operator (GNO) that leverages…

Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…

Neural Operators (NOs) are a leading method for surrogate modeling of partial differential equations. Unlike traditional neural networks, which approximate individual functions, NOs learn the mappings between function spaces. While NOs have…

The recent development of Neural Operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this paper,…

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks…

Solving partial differential equations remains a central challenge in scientific machine learning. Neural operators offer a promising route by learning mappings between function spaces and enabling resolution-independent inference, yet they…

Acquisition of large datasets for three-dimensional (3D) partial differential equations (PDE) is usually very expensive. Physics-informed neural operator (PINO) eliminates the high costs associated with generation of training datasets, and…

Implicit Neural Representations (INRs) are widely used for modeling continuous 2D images, enabling high-fidelity reconstruction, super-resolution, and compression. Architectures such as SIREN, WIRE, and FINER demonstrate their ability to…

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…

Recently deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we…

Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated that incorporating Lie point symmetry information can…

Neural operators generalize neural networks to learn mappings between function spaces from data. They are commonly used to learn solution operators of parametric partial differential equations (PDEs) or propagators of time-dependent PDEs.…

This article introduces GIT-Net, a deep neural network architecture for approximating Partial Differential Equation (PDE) operators, inspired by integral transform operators. GIT-NET harnesses the fact that differential operators commonly…

Solving high-dimensional partial differential equations (PDEs) efficiently requires handling multi-scale features across varying resolutions. To address this challenge, we present the Multiwavelet-based Multigrid Neural Operator (M2NO), a…

Increased demands for high-performance materials have led to advanced composite materials with complex hierarchical designs. However, designing a tailored material microstructure with targeted properties and performance is extremely…

We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks…

In this paper, we propose a way to solve partial differential equations (PDEs) by combining machine learning techniques and the finite element method called Phi-FEM. For that, we use the Fourier Neural Operator (FNO), a learning mapping…

Accurate modeling of personalized cardiovascular dynamics is crucial for non-invasive monitoring and therapy planning. State-of-the-art physics-informed neural network (PINN) approaches employ deep, multi-branch architectures with…

Accurate and efficient physical simulations are essential in science and engineering, yet traditional numerical solvers face significant challenges in computational cost when handling simulations across dynamic scenarios involving complex…

Accurate urban microclimate analysis with wind velocity and temperature is vital for energy-efficient urban planning, supporting carbon reduction, enhancing public health and comfort, and advancing the low-altitude economy. However,…